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If a number has prime factorisation (2^a\times3^2\times5) and it has (24) total factors, what is the value of (a)?
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Answer and explanation
Correct answer: (3)
Step 1: Total factors are ((a+1)(2+1)(1+1)). Step 2: ((a+1)\times3\times2=24), so (a+1=4) and (a=3). Step 3: For an unknown exponent, apply the factor-count rule directly.
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What is the correct answer to this question?
(3)
Why is this the correct answer?
Step 1: Total factors are ((a+1)(2+1)(1+1)). Step 2: ((a+1)\times3\times2=24), so (a+1=4) and (a=3). Step 3: For an unknown exponent, apply the factor-count rule directly.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Real Numbers. Topic: Prime Factorisation.
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